In this study, a numerical approach was developed to approximate the solution of the Caputo-type fractional reaction–diffusion problem. In the proposed method, the Caputo fractional derivative and the ...

We developed a physics-informed neural network based on a mixture of Cartesian grid sampling and Latin hypercube sampling to solve forward and backward modified diffusion equations. We optimized the ...

“However, to compare model predictions with empirical observations, one needs to study the diffusion equation in finite space. Despite the work of illustrious scientists such as Smoluchowski, Pólya, ...